Re: What Flows?

I don't think anyone has suggested deliberately lying to students (at
least, I hope not). My reading of this discussion has been more in
terms of a recognition that a simple assertion of a fact without a
context within which the student can see that it is a necessary one.

I thought I had given you a perfectly good context within which the
student *must* use the concepts correctly to get the correct answer.

I thought of it (see below) as a context within which the student can
discover what the correct concepts are.

In other words, a student learns primarily (if not exclusively) by
discovering that his/her current conceptions have failed in analyzing
the current problem and then trying to replace them with more precise
and useful conceptions. This is in fact exactly the thrust of the
example you have given in which a hypothetical student confronts an
inconsistency between two colloquially held ideas. THEN you have an
opportunity to teach but before that confrontation occurs, most of
the time you do not. It goes in one ear and out the other as you
haven't got any phenomenon for your words to latch onto in the
student's mind.

Since you are going to introduce the concepts anyway, what is to be
gained by introducing the wrong ones first? I think the answer is
that nothing is to be gained. The student will never understand the
resolution of that particular paradox (the adiabatic equilibrium of
the atmosphere) without the correct definition. Would you say "As the
air rises it loses thermal energy" or "its thermal energy decreases"?
Would you say "There is a flow of heat out of the air as it rises"!?
All of those are, I hope you will agree, very wrong. Please tell us
how you are going to reconcile this apparent contradiction using the
flawed concepts you claim are satisfactory for use by beginners.

Leigh

If you read back over what I wrote, I never made that claim. In fact
_I_ am _not_ going to reconcile the contradiction. I am instead going
to ask my _student_ to do so. Learning takes place in the mind of the
student, not the teacher. Why then should the teacher be the only
active one in reconciling this conundrum?

Again, I think there is a bit of missed communication here (either
that or you are setting up a straw man but I don't think you would do
that). The argument is not over whether one should introduce flawed
ideas and then modify them over time into more nearly correct ones
but rather over how one should go about introducing correct (or
nearly correct) ideas. If I have to start with the best physics I
know, then I would have to start my mechanics class on quantum theory
and that would be silly. Instead, I have to build outward based on
the flawed ideas that _the students bring with them_. To do that, I
have to present them with a series of situations in which those
preconceptions _fail_ and then ask the _student_ to resolve that
failure.

Eventually, this of course requires the introduction and consistent
use of rigorous terminology. After all, language is the medium in
which we think, like a wave in water, and if the language remains
sloppy the thinking is more likely to be sloppy as well. In fact,
some have argued that thought is really little more than linguistics
(e.g. Julian Jaynes in _The Origin of Consciousness in the Breakdown
of the Bicameral Mind_ where he conceives of thought as primarily
metaphor construction). But I have never been successful at enforcing
linguistic rectitude by fiat. Rather, students do not seem to be able
to consistently use precise terminology until after they have
explicitly discovered the need to make precise discriminations. For
example, I usually have students use 9.8 for everything having to do
with gravity, and in fact calling it gravity, until they try to use
it for a gravitational force (conveniently omitting the units)
and get a patently silly answer. I do consistently refer to it as an
acceleration and insist that they do so as well but they are not
consistent about it until they discover the need for such
discrimination themselves.

This is not a matter of introducing wrong concepts. Rather, it is a
matter of how you get to introducing the right ones -- as a discovery
or as a sermon. The former will stick, the latter generally does not.

Paul J. Camp "The Beauty of the Universe
Assistant Professor of Physics consists not only of unity
Coastal Carolina University in variety but also of
Conway, SC 29528 variety in unity.
pjcamp@csd1.coastal.edu --Umberto Eco
pjcamp@postoffice.worldnet.att.net The Name of the Rose
(803)349-2227
fax: (803)349-2926